First of all, here's a good article on ripple rejection. It has the formula right in the first page, so you can solve for Ripple[output] if you have the PSRR.
Am I right in thinking that I can just leave JP5 (tracking pre-regulator feedback) unconnected until I'm clever enough to make one?
So I just put my nice, smooth 24v into both JP1 (power input) and JP8 (LM324 supply)?
I'm slightly confused by JP2 & JP4 (voltage & current inputs). When you say "1v in = ...", do you mean putting an additional, separate voltage source in, or do you mean simply changing what's there through a multi-turn potentiometer? If so, what values do you recommend?
JP5 is there to give you the current output voltage even if the fuse F1 is broken (hopefully to make troubleshooting easy), it is useful for tracking pre-regulators because these need to know the output voltage to set the input voltage. You can leave it disconnected.
You can feed JP1 and JP8 straight from the rectified and smoothed power rail you have. Just be careful when the power supply is not loaded with anything because the voltage on JP8 and JP1 will be higher and if gets over 32V it can damage the LM324.
If the output ripple is unacceptable (I would aim for 10mV at 1A) you can try reducing the ripple by adding more capacitance after your rectifier or you can try to filter the voltage only on JP8 using an LC filter like smashedProton said. The second option should be cheaper and smaller.
If Amspire's power supply had -40dB ripple rejection (I am sure it is closer to -60dB), 1V of input ripple would be 10mV on the output. At -50dB it would be 3mV. At -60dB is would be 1mV.
Wikipedia has a handy table on decibels. Use the amplitude ratio in this case:
http://en.wikipedia.org/wiki/DecibelJP2 and JP4 are used to set the output current and voltage. Let's say you feed 1V on each of those. For now ignore where that volt comes from. The output would be 10V with a 1A current limit. If you feed 0.5V on JP2 and 0.1V on JP4 you get 5V on the output and the current limit set to 100mA.
Where do we get these voltages from? It's your choice. If you want to use a multiturn pot, you connect the wiper pin to JP2/JP4, the first pin to GND and the third pin to 2V if you are using JP2 or 1V if you are using JP4.
You can get the 2V with an LM317. The 1V is trickier to get because the LM317 goes down to only 1.25V. Take the 2V reference and divide it in half with a voltage divider. Buffer that with an LM358 configured as a voltage follower and connect the current pot to that. Feed the LM358 with more than 5V but less than 32V, you can use the 24V you have. If you are not going to use the second op-amp included in the chip, configure it as a voltage follower too, but leave the output disconnected.
The good thing about this power supply is that you can upgrade stuff. If you want, you can build the tracking pre-regulator later.